Number Talks: A Powerful Math
Instructional Practice
Why Talk About Math
“ Our classrooms are filled with students and adults who think
of mathematics as rules and procedures to memorize without
understanding the numerical relationships that provide the
foundation for these rules.”
What is a number talk?
 Goal: The goal of a number talk is to build computational
fluency.
 Computational fluency: having an efficient and accurate method
for computing
Principal and Standards for School mathematics, NCTM, Reston, VA
2000, p.152
Why do we do Number Talks?
 It allows children the opportunity to engage in rich
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meaningful conversations.
Students have a chance to share and explain strategies.
Justify answers
Think and act like mathematicians
Mental Math
Number Talks!
• Done daily
• Separate from your other math block
• 10-15 minutes
• Meaningful conversations
• No pencil and paper
• No manipulatives (optional)
• Does not replace your current math curriculum
• Small group or whole group
Steps to Number Talks
 Present the problem
 Allow for quiet think time
 Thumbs up when ready
 Students share their answers
 Teachers record all possible solutions
 Students share their strategies (3-4)
Number Talks in Action
Before we watch the third grade number talk for 70-34, think about
how you would mentally solve this problem.
As you are viewing the video clip, consider the following:
1.
2.
3.
4.
How are students using number relationships to solve the
problem?
How would you describe the classroom community and
environment?
Which strategies demonstrate accuracy, efficiency, and
flexibility?
How are the students’ strategies similar or different from your
strategy?
The Key Components of Number Talks
1.
2.
3.
4.
5.
Classroom environment and community
Classroom discussions
The teacher’s role
The role of mental math
Purposeful computation problems
Classroom Environment and
Community
 Safe, risk-free environment
 Students comfortable and offer responses for discussion
 Classroom exhibits a culture of acceptance based on the
common goal of learning and understanding
 Community of learners based on mutual respect
Classroom Discussions
 Develop system for students to respond to questions, while
allowing for think time.
 What did we see in the video clip?
The Teacher’s Role
• “Since the heart of number talks is classroom conversations, it is
appropriate for the teacher to move into the role of facilitator.”
• Teachers must change their thinking from concentrating on
the final correct answer, to listening and learning about
students’ natural thinking through asking open ended
questions.
• “What answer did you get?” “How did you get your answer?”
The Role of Mental Math
 Students need to approach problems without paper and
pencil, and are encouraged to rely on what they know and
understand about numbers and how they are related.
 Mental computation helps students strengthen their
understanding of place value.
Purposeful Computation Problems
 Careful planning BEFORE the number talk is necessary to
design “just right” problems for students.
 This planning is important because we want to have a
purposeful number talk with a common focus/specific skill
in mind.
Establishing Procedures and Setting
Expectations: The Four Essentials
The number talk is designed to be only five to ten minutes of focused
discussion.
1. Select a designated location that allows you to maintain
close proximity to your students for informal observations
and interactions.
2. Provide appropriate wait time for the majority of the
students to access the problem.
3. Accept, reject, and consider all answers.
4. Encourage student communication throughout the
number talk.
Holding Students Accountable for their
Learning
1.
2.
3.
4.
5.
6.
Ask students to use finger signals to indicate the most
efficient strategy.
Keep records of problems posed in the corresponding
student strategies.
Hold small-group number talks every day.
Create and post class strategy charts. (living document)
Require students to solve an exit problem using the
discussed strategies. (use an index card)
Give a weekly computation assessment.
Hand Signals
Let’s Try It
I’ve got a
solution
I’ve got a 2nd
solution
 Procedures
 “I’m thinking”
 “I have a solution”
I’ve got a 3rd I agree with
solution
you
 “I agree”
 Solutions
 Recording Student Thinking
Four Goals for K-2 Number Talks
1.
Developing number sense
“Number sense is an awareness and understanding about what
numbers are, their relationships, their magnitude, the relative effect
of operating on numbers, including the use of mental mathematics
and estimation.”
Developing fluency with small numbers
3. Subitizing (immediately recognizing a collection of objects
as a single unit)
4. Making tens
2.
Classroom Link: Ten-Frames and Dot Cards
Classroom Clip: Kindergarten
Consider the following while viewing the clip:
1. How does the teacher build student fluency with small numbers?
2. What questions does the teacher pose to build understanding?
3. How are the tools and models used to support the goals of K-2
number talks?
4. What strategies are the students using to build meaning of the
numbers?
5. What examples of subitizing, conserving number, and one-to-one
correspondence do you notice?
6. What opportunities are created for the students to begin building an
understanding of ten?
7. How does the teacher support student communication during the
number talk?
Classroom Link: Ten-Frames: 8+6
Classroom Clip 2nd grade
Consider the following while viewing:
1. How does the teacher build student fluency with small
numbers using ten-frames?
2. What questions does the teacher use to build understanding
about decomposing and composing?
3. How are the double ten-frames used to support the goals of K2 number talks?
4. What strategies are the students using to build meaning of the
numbers?
5. What opportunities are created for the students to understand
and use 10 as a unit?
6. How do the students demonstrate composing and decomposing
numbers?
Five Goals for Number Talks 3-5
1.
2.
3.
4.
5.
Number sense
Place value
Fluency
Properties
Connecting mathematical ideas
Classroom Link: Subtraction: 1000-674
Classroom Clip 5th Grade
As you watch the video, consider the following:
1. What evidence in the video supports student
understanding of place value?
2. How do the students’ strategies exhibit number sense?
3. How does fluency with smaller numbers connect to the
students’ strategies?
4. Which strategies were most accessible to you? More
challenging to follow?
5. How are accuracy, flexibility, and efficiency interwoven in
the students’ strategies?
Bringing It All Together:
Number Talks from the Schoolwide Perspective
“We have just taken a journey of number talks from kindergarten
through the fifth grade by viewing video clips and group discussions.
While teacher personalities and environments may change as students
transition from grade level to grade level, essential number talk
content and characteristics remain consistent from year to year.This
consistency in teaching mathematically big ideas, instruction rooted
in asking rather than telling, developing a safe learning community,
and an unwavering quest for making sense are essential in building
mathematically powerful students.The consistency from grade level to
grade level does not occur by coincidence; it is purposefully
orchestrated by the school learning community.”
Looking at Mathematics through a
Common Core Lens
Our goal as educators is to help students to become confident and
competent in mathematics. We strive to create a classroom
environment that encourages students to think critically about
math in a variety of situations. As students explain their thinking
to others, they self-correct and clarify their ideas leading to a
deeper understanding of underlying mathematical concepts.
Accuracy and the development of efficient problem-solving
strategies are essential to student’s learning. The ability to solve
problems many different ways and to understand the connections
between mathematical ideas is equally important. As children
learn to question, reconsider and justify solutions they become
more confident in their own abilities as mathematicians.
Questions??
Are there any questions before we do a number talk?
Lets try one!
Number Talk!
39 + 17 =
Number Talk!
Number Talks!
 Thumbs up when you are ready!
 How many dots did you see?
 How did you figure that out?
Number Talk!
123 + 79 =